Textbook Problem

Health After a person exercises for a few minutes, the velocity v (in liters per second) of airflow into and out of the lungs during a respiratory cycle is given by

$v=1.75\sin \frac{\pi t}{2}$ where t is the time (in seconds). Inhalation occurs when v > 0, and exhalation occurs when v < 0.

(a) Find the time for one full respiratory cycle.

(b) Find the number of cycles per minute.

(c) Find the velocities of airflow when t = 2 and t = 3 without using a calculator.

(d) Use a graphing utility to find the velocity of airflow when t = 1.5.

(e) Use a graphing utility to graph the velocity function.